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a) Determine the transfer function associated with Eq.(4.1). b) The dynamic response of the system is controlled using a PI controller: PI The transfer function of the PI controller is Beam Fig. Q4.2 Closed-loop system K₁ C(s)= a(K₁ +) e(s) with K₁=2, K₁= 5 and = 1. Determine the open-loop transfer function and the associated frequency response function. c) Determine the closed-loop transfer function.

a) Determine the transfer function associated with Eq.(4.1). b) The dynamic response of the system is controlled using a PI controller: PI The transfer function of the PI controller is Beam Fig. Q4.2 Closed-loop system K₁ C(s)= a(K₁ +) e(s) with K₁=2, K₁= 5 and = 1. Determine the open-loop transfer function and the associated frequency response function. c) Determine the closed-loop transfer function.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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to Fig. Q4.1 Rigid beam An engineer is studying the small vibration of the rigid beam depicted in Fig.Q4.1 around its rest position. The beam is linked to the support using a rotational spring. It can be shown that the angle is given by the solution of the equation JÖ + a0 + k₂0 = →i (s) 0 where J = 500 kgm² is the moment of inertia, a = 100 Nsm/rad is the damping coefficient, ke = 1200Nm/rad is the rotational stiffness, L=1m is the length of the beam and f(t) is an applied force. a) Determine the transfer function associated with Eq.(4.1). b) The dynamic response of the system is controlled using a PI controller: Lf(t) PI The transfer function of the PI controller is Fig. Q4.2 Closed-loop system Beam C(s) = a(K₁, + K₁ ↓ f(t) S ) e(s) with K₁=2, K₁= 5 and = 1. Determine the open-loop transfer function and the associated frequency response function. c) Determine the closed-loop transfer function.
Transcribed Image Text:to Fig. Q4.1 Rigid beam An engineer is studying the small vibration of the rigid beam depicted in Fig.Q4.1 around its rest position. The beam is linked to the support using a rotational spring. It can be shown that the angle is given by the solution of the equation JÖ + a0 + k₂0 = →i (s) 0 where J = 500 kgm² is the moment of inertia, a = 100 Nsm/rad is the damping coefficient, ke = 1200Nm/rad is the rotational stiffness, L=1m is the length of the beam and f(t) is an applied force. a) Determine the transfer function associated with Eq.(4.1). b) The dynamic response of the system is controlled using a PI controller: Lf(t) PI The transfer function of the PI controller is Fig. Q4.2 Closed-loop system Beam C(s) = a(K₁, + K₁ ↓ f(t) S ) e(s) with K₁=2, K₁= 5 and = 1. Determine the open-loop transfer function and the associated frequency response function. c) Determine the closed-loop transfer function.
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